Question

is figure abcd congruent to figure pqrs? no, figure abcd is congruent to figure klmn. yes, rotate figure abcd 270° about the origin and then translate it 3 units up. yes, rotate figure abcd 90° about the origin and then translate it 3 units down. yes, translate figure abcd 1 unit down and 10 units left.

Explanation:

Step1: Recall congruence concept

Two figures are congruent if they have the same shape and size. Rigid - motions (rotations, translations, reflections) preserve congruence.

Step2: Analyze each option

• Option 1: Just stating congruence without a transformation doesn't show how they are related.
• Option 2: A 270 - degree rotation about the origin and then a 3 - unit up translation is a rigid - motion. Rotation and translation are rigid - motions that preserve the shape and size of the figure.
• Option 3: A 90 - degree rotation about the origin and then a 3 - unit down translation is a rigid - motion.
• Option 4: Translating 1 unit down and 10 units left is a rigid - motion.

All the transformation - based options (2, 3, 4) imply congruence since they are rigid - motions. But we need to answer the congruence question first. Since rigid - motions can map one figure onto the other, Figure ABCD is congruent to Figure PQRS.

Answer:

Yes, rotate Figure ABCD 270° about the origin and then translate it 3 units up; Yes, rotate Figure ABCD 90° about the origin and then translate it 3 units down; Yes, translate Figure ABCD 1 unit down and 10 units left; Yes, Figure ABCD is congruent to Figure PQRS.